We chose not to put controller support into the button builder demo due to the contact-heavy nature of the experience. All of the Interaction Engine Example Scenes (available inside of the InteractionEngine folder inside of LeapMotion/Modules) support controllers (and automatic switching between controller and hand tracking systems).
If you would like to test controller support in Button Builder anyway, you can take the InteractionManager (with child controller assets) from one of the example scenes in the InteractionEngine and replace the one in Button Builder with it.
You'll also want to ensure "Ignore Grasping" is disabled on the UI Elements that you would like to be able to "Grab" with your controller.
EDIT: Hmm, it appears there are some issues relating to importing the package into fresh projects that are affecting the behavior of the controllers; fixes and warnings for these will be included in a hot-fix due out later today. In the mean-time, ensure that your LeftVRTriggerAxis and RightVRTriggerAxis are set up in your InputManager to the 9th and 10th Joystick Axes respectively (or use the UnityModules repo which has these settings already).